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Question

If α,β are zeroes of the polynomial p(x)=x2x4, then find the value of αβ+βα+3(1α+1β)2αβ..

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Solution

Given, α,β are zeroes of the polynomial p(x)=x2x4, Then from the relation between the relation roots and co-efficients we get,
α+β=1.....(1) and α.β=4......(2).
Now,
αβ+βα+3(1α+1β)2αβ
=α2+β2α.β+3α+βα.β2α.β
=(α+β)22α.βα.β+3α+βα.β2α.β
=9434+8 [ Using (1) and (2)]
=3+8
=5.

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